Linear Degenerate Tropical Flag Varieties
Alessio Borz\`i, Victoria Schleis

TL;DR
This paper explores linear degenerations of flag varieties through tropical geometry, establishing correspondences between various mathematical structures such as valuated matroids and tropical linear spaces.
Contribution
It introduces the linear degenerate flag Dressian and proves a new correspondence linking degenerations, valuated matroids, and tropical linear spaces.
Findings
Defined the linear degenerate flag Dressian.
Established a correspondence between points in the Dressian and degenerations.
Connected degenerations with morphisms of valuated matroids.
Abstract
We study linear degenerations of flag varieties from the point of view of tropical geometry. We define the linear degenerate flag Dressian and prove a correspondence between: points in the linear degenerate flag Dressian, linear degenerate flags of valuated matroids, linear degenerate flags of tropical linear spaces, and morphisms of valuated matroids arising from projection maps.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsPolynomial and algebraic computation · Advanced Topics in Algebra · Advanced Differential Equations and Dynamical Systems
